We need to find the surface area of a cylinder with a radius of 8 yd and a height of 6 yd. This cylinder and its lateral surface are shown below:
Notice that its lateral surface corresponds to a rectangle with a width equal to the height of the cylinder, and a length equal to the perimeter of the cylinder's base.
Thus, the lateral surface area is given by:
[tex]6\text{ yd}\cdot2\pi8\text{ yd }=96\pi\text{ yd}^2[/tex]And the area of each base is the area of a circle with a radius of 8 yd:
[tex]\pi(8\text{ yd})^2=64\pi\text{ yd}^2[/tex]Since it has a top and a bottom base, we need to multiply the last result by two and then add it to the lateral surface area to find the total surface area. We obtain:
[tex]2\cdot64\pi\text{ yd}^2+96\pi\text{ yd}^2=224\pi\text{ yd}^2[/tex]If we approximate the answer to one decimal place, we obtain:
[tex]703.7\text{ yd}^2[/tex]Answer: Approximately 703.7 yd²
